A sparse effective Nullstellensatz

Details A sparse effective Nullstellensatz A sparse effective Nullstellensatz

1997-10-01

arxiv.org/abs/alg-geom/9710003v1

Mathematics

Commutative Algebra

24 pages, Latex2e, available at http://www.dm.uba.ar/tera/ and http://hilbert.matesco.unican.es/tera/

Scientific paper

We present bounds for the sparseness and for the degrees of the polynomials in the Nullstellensatz. Our bounds depend mainly on the unmixed volume of the input polynomial system. The degree bounds can substantially improve the known ones when this polynomial system is sparse, and they are, in the worst case, simply exponential in terms of the number of variables and the maximum degree of the input polynomials.

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